Answer:
She travels 30 miles for work.
Given,
Total time = 45 minutes
Speed on small world = 32mph
Time on small world = 1/2 hour
Distance = Speed * time =
Distance on small world = 16 miles
Speed on small road = 56mph
Time on small road = 1/4 hour
Distance on small road =
Distance on small road = 14 miles
Total distance = Distance on small world + Distance on small road
Total distance = 16+14= 30 miles
She travels 30 miles for work.
Keywords: Distance, speed
Step-by-step explanation:
Final answer:
Carol travels 12 miles on the small road and 28 miles on the highway, totaling 40 miles to get to work.
Explanation:
The question asks us to calculate the total distance Carol travels to work using two different speeds on two different roads. To solve this problem, we use the formula d = vt, where d represents distance, v is velocity (or speed), and t is time.
On the small road, Carol drives at 24 miles per hour for half an hour (0.5 hours). Therefore, the distance traveled on the small road is:
d = (24 miles/hour)(0.5 hours) = 12 miles
On the highway, she drives at 56 miles per hour for half an hour (0.5 hours) as well. The distance traveled on the highway is:
d = (56 miles/hour)(0.5 hours) = 28 miles
To find the total distance, we add the distances from both roads:
Small road: 12 milesHighway: 28 milesTotal distance = 12 miles + 28 miles = 40 miles
Carol travels a total of 40 miles to get to work.
Rewrite the expression using only positive integer exponents.
The value of the expression is [tex]\frac{m^4}{n^2}[/tex].
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex](m^{2/3}n^{-1/3})^6[/tex]
This can be simplified as,
[tex]m^{2/3 \times6}[/tex] x [tex]n^{-1/3 \times 6}[/tex]
=[tex]m^{2\times2}[/tex] x [tex]n^{-1 \times2}[/tex]
= [tex]m^4[/tex][tex]n^{-2}[/tex]
= [tex]\frac{m^4}{n^2}[/tex]
Thus,
The value is [tex]\frac{m^4}{n^2}[/tex].
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ5
To rewrite an expression using only positive integer exponents, apply the rules of exponentiation and simplify the expression.
Explanation:To rewrite an expression using only positive integer exponents, you can apply the rules of exponentiation. For example, if you have an expression like [tex]a^{-2}[/tex], you can rewrite it as [tex]\frac{1}{a^{2} }[/tex]
. Similarly, if you have a term with a negative exponent in the denominator, you can move it to the numerator and change the sign of the exponent to make it positive.
Here's a step-by-step example:
Start with the original expression. If there are negative exponents present, move them to the numerator or denominator as needed.Change the sign of the exponent to make it positive.Simplify the expression if possible.By following these steps, you can rewrite expressions using positive integer exponents.
Learn more about Rewriting expressions here:https://brainly.com/question/33931683
#SPJ13
Question 1 0 / 5 pts (06.07A LC) The legs of a right triangle are 3 units and 8 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. (5 points) 8.54 units 9.54 units 11.00 units 24.00 units
Question 2 5 / 5 pts (06.07A LC) Jacob calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle was it? (5 points) A B C D
Question 3 5 / 5 pts (06.07A MC) What is the length of the third side of the window frame below? (5 points) (Figure is not drawn to scale.) 15 inches 27 inches 25 inches 32 inches
Question 4 5 / 5 pts (06.07A MC) The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown. (Figure is not drawn to scale.) Which of the following options is closest to the distance (in miles) between points A and B? (5 points) 2.24 miles 2.65 miles 3.74 miles 5.29 miles
Answer: H
Step-by-step explanation:Question 1(Multiple Choice Worth 5 points) (06.07A MC) What is the length of the third side of the window frame below? (Figure is not drawn to scale.) A picture of a right triangular window frame is shown. The longest side has length labeled as 87 inches. The height of the frame is labeled as 63 inches. 48 inches 60 inches 70 inches 75 inchesanswer - 60Question 2(Multiple Choice Worth 5 points) (06.07A MC) The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown. (Figure is not drawn to scale.) A picture of a right triangle ABC with right angle at B is shown. The length of the side AC is labeled as 9 miles. The length BC of the triangle is labeled as 6 miles. This length BC is also the length of an irregular gray shaded shape. Which of the following options is closest to the distance (in miles) between points A and B? 6.71 miles 7.35 miles 8.66 miles 10.82 miles answer - 6.71Question 3(Multiple Choice Worth 5 points) (06.07A LC) The legs of a right triangle are 3 units and 8 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. 8.54 units 9.54 units 11.00 units 24.00 units answer - 8.54Question 4(Multiple Choice Worth 5 points) (06.07A LC) Jessica calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle was it? Four triangles E, F, G, H are shown from left to right. Triangle E has one side labeled as 2 and the other as 3, and the included acute angle is shown. Triangle F has both sides labeled as 3, and the included acute angle is shown. Triangle G has one side labeled as 4 and the other as 2, and the included right angle is shown. Triangle H has one side labeled as 6 and the other as 7, and the included obtuse angle is shown. answer h
What is the answer to this
To calculate the height of a tree, Ryan measures the
angle of elevation from a rock on the ground to be 34°
He measures his distance from the rock on the ground
to the base of the tree to be 8 meters. How high is the
tree to the nearest tenth of a meter?
The height of the tree is 5.4 m
Step-by-step explanation:
Let the height of the tree be 'h'
Angle of elevation= 34°
distance from the rock on the ground
to the base of the tree = 8 m
we can use the tan function of trigonometry to find the height of the tree,
tan 34° = h/8
tan 34° = 0.67
tan 34° = h/8
0.67 = h/8
h = 8 x 0.67
h = 5.4m
The height of the tree is 5.4 m
The height of the tree to the nearest tenth of a meter is approximately 5.6 meters.
To calculate the height of the tree, we can use trigonometry, specifically the tangent function since we have the angle of elevation and the distance from the observer to the base of the tree.
Let's denote:
h as the height of the tree,d as the distance from the observer to the base of the tree.According to trigonometry,
[tex]\[ \tan(\text{angle of elevation}) = \frac{\text{height of the tree}}{\text{distance to the tree}} \][/tex]
Substituting the given values:
[tex]\[ \tan(34^\circ) = \frac{h}{8} \][/tex]
Now, let's solve for h:
h = 8 × tan(34°)
Using a calculator, we find:
h ≈ 8 × 0.6947
≈ 5.5576
Therefore, the height of the tree to the nearest tenth of a meter is approximately 5.6 meters.
When proving the product, quotient, or power rule of logarithms, various properties of logarithms and exponents must be used.
Which property listed below is used in all of these proofs?
Answer:
d
Step-by-step explanation:
Which phrase is a hit about what might happen later in the story?
Answer:
foreshadowing
Step-by-step explanation:
Is that what you're looking for?
If it is:
Foreshadowing includes the clues the author throws into a story to hint at what may happen in the future, or further in the book. For instance, Character A says to Character B that "I've never broken a bone before! I've never even been hospitalized" but does so near the climax of the story.
which answer choice shows the number four hundred sixty -five ten - thousandths in standard from
Answer:
4.65 x 10^-5
Step-by-step explanation:
.00465
[tex]4.65 x 10^{-5}[/tex]
Quadrilateral DUCK is inscribed in circle O what is the measure of
Answer:
95°
Step-by-step explanation:
Since, quadrilateral DUCK is inscribed in circle O
sum of the opposite angles of the quadrilateral is 180°
m<K +m<U= 180°
m<K= 180°- 85°= 95°
Answer:
95 degrees
Step-by-step explanation:
Quadrilaterals that are inscribed in circles are often called "cylic". Cyclic quadrilaterals have many unique properties. One of these is that opposite angles add up to 180 degrees.
Here, DUCK is a cyclic quadrilateral. "Opposite angles" are < U and < K, as well as < D and < C. So, since < U and < K are opposite angles in this inscribed quadrilateral, they add up to 180 degrees:
< U + < K = 180
We already know that < U = 85, so:
85 + < K = 180
< K = 95
Thus, < K is 95 degrees.
Hope this helps!
Which statement could be used to describe the functions?
O Both original functions have a domain of (-0,-).
O Both original functions have a domain of [-0, 2).
The domain of f(x) is [2, o), while the domain of g(x) is
(-0, 2]
O The domain of f(x) is (-00, 2], while the domain of g(x)
is [2, 0).
Answer:
number d im (pretty sure)
Step-by-step explanation:
GUEST
An equation is given.
6-x=y
Complete the table to show the relationship between values of x and y.
O
2
Answer: 6 and 4
Step-by-step explanation:
Fill in the numbers with the correct variable and you get your answer. 6-0=6 6-2=4
|7m+4| =1 pls pls.
|7m + 4| = 1
It can equal either 1 or -1, so:
7m + 4 = 1
7m = -3
m = -3/7
7m + 4 = -1
7m = -5
m = -5/7
Leah has just inherited 12000 she wants to invest the money so that she can increase the value of her inheritance what are some of the ways she can do this
Answer:
she can put it in a bank to gain interest
she can invest in the stock market
she can loan out money
Step-by-step explanation:
Depending on the compounding frequency, Leah's investment of $12,000 with a 4.5% annual interest rate would yield the following amounts after 10 years:
- Continuous compounding: approximately $18,843.48
- Daily compounding: approximately $19,212.03
- Monthly compounding: approximately $18,867.02
Leah's inheritance presents her with a golden opportunity to grow her wealth through strategic investment. With $12,000 at her disposal, she can explore various avenues to maximize the value of her funds. One option she's considering is investing in an account that offers a 4.5% annual interest rate.
To evaluate the potential returns from this investment, she needs to understand how different compounding frequencies affect the growth of her investment over time.
Let's start by defining the equations for the amount A(t) in the account after t years, using continuous compounding, daily compounding, and monthly compounding.
1. Continuous Compounding:
The formula for continuous compounding is given by:
[tex]\[ A(t) = P \times e^{rt} \][/tex]
where:
- A(t) is the amount of money in the account after t years,
- P is the principal amount (initial investment),
- r is the annual interest rate (expressed as a decimal),
- t is the time in years, and
- e is the base of the natural logarithm, approximately equal to 2.71828.
Using Leah's values:
P = $12,000
r = 0.045 (4.5% expressed as a decimal)
Substituting these values into the formula, we get:
[tex]\[ A(t) = 12000 \times e^{0.045t} \][/tex]
To find the amount after 10 years, we can plug t = 10 into the equation and calculate the result.
[tex]\[ A(10) = 12000 \times e^{0.045 \times 10} \][/tex]
[tex]\[ A(10) \approx 12000 \times e^{0.45} \][/tex]
[tex]\[ A(10) \approx 12000 \times 1.57029 \][/tex]
[tex]\[ A(10) \approx \$18,843.48 \][/tex]
So, after 10 years of continuous compounding, Leah's investment would be approximately $18,843.48.
Next, let's consider daily compounding. In this case, interest is compounded 365 times per year, so the formula becomes:
[tex]\[ A(t) = P \times \left(1 + \frac{r}{365}\right)^{365t} \][/tex]
Using the same values as before, we can calculate:
[tex]\[ A(10) = 12000 \times \left(1 + \frac{0.045}{365}\right)^{365 \times 10} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + \frac{0.045}{365}\right)^{3650} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + 0.00012328767123\right)^{3650} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.00012328767123)^{3650} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.60100220887) \][/tex]
[tex]\[ A(10) \approx \$19,212.03 \][/tex]
After 10 years of daily compounding, Leah's investment would be approximately $19,212.03.
Finally, let's explore monthly compounding. With monthly compounding, interest is compounded 12 times per year, so the formula becomes:
[tex]\[ A(t) = P \times \left(1 + \frac{r}{12}\right)^{12t} \][/tex]
Using the same values as before, we can calculate:
[tex]\[ A(10) = 12000 \times \left(1 + \frac{0.045}{12}\right)^{12 \times 10} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + \frac{0.045}{12}\right)^{120} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + 0.00375\right)^{120} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.00375)^{120} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.5722520173) \][/tex]
[tex]\[ A(10) \approx \$18,867.02 \][/tex]
After 10 years of monthly compounding, Leah's investment would be approximately $18,867.02.
In summary, depending on the compounding frequency, Leah's investment of $12,000 with a 4.5% annual interest rate would yield the following amounts after 10 years:
- Continuous compounding: approximately $18,843.48
- Daily compounding: approximately $19,212.03
- Monthly compounding: approximately $18,867.02
These calculations illustrate how different compounding frequencies can affect the growth of an investment over time. Daily compounding typically results in slightly higher returns compared to monthly compounding, while continuous compounding offers the highest potential returns due to its continuous nature.
By understanding these dynamics, Leah can make an informed decision about how to maximize the growth of her inheritance based on her investment preferences and goals.
The complete question is:
Leah has just inherited $12,000. She wants to invest the money so that she can increase the value of her inheritance. What are some of the ways she can do this?
1. Leah wants to invest the $12,000 in an account that pays 4.5% annual interest.
a. Write equations for the amount A(t) that will be in the account after t years, if the interest is
compounded continuously, daily, and monthly. Then, find the amount after 10 years, rounded
to the nearest cent, for each method of compounding.
A mirror has a diameter of 14 inches what is the radius and unit of measure
Answer:
The radius is 7 inches
Step-by-step explanation: The radius is half of the diameter and the unit of measure is inches. Unit of measurement includes inches, centimetres, meters, kilometres, etc.
Find the sum or difference.
(6x + 5) + (-3x + 7)
Answer:
3x+12 is the sum
9x-2 is differences
Step-by-step explanation: Combine like terms
express the first quantity as a percentage of the second
a) 35 minute 2 hour
b )650g.3 kg
Answer:
a) 29% b) 22%
Step-by-step explanation:
The quantities must be expressed in the same units.
a) compare 35 minutes to 2 hours. 2 hours is 2 x 60 = 120 minutes.
35/120 = .291667 = 29%
b) compare 650 grams to 3 kilograms. 3 kg = 3 x 1000 = 3000 g.
650/3000 = .21667 = 22%
Answer:
see explanation
Step-by-step explanation:
To express as a percentage, first express as a fraction and multiply by 100%
The quantities must be expressed in the same units.
(a)
2 hours = 2 × 60 = 120 minutes, thus
[tex]\frac{35}{120}[/tex] × 100% ≈ 29.2% ( to 1 dec. place )
(b)
3 Kg = 3 × 1000 = 3000 g, thus
[tex]\frac{650}{3000}[/tex] × 100% ≈ 21.7% ( to 1 dec. place )
How many leaves are there if you have 9 clovers?
Answer:
36 leaves
Step-by-step explanation:
1 clover has 4 leaves
so if you have 9 clovers multiply the leaves by clovers by 4
1:4
9:36
4 + x/7 = 2 plz solve
Answer x=-14.
Step-by-step explanation:
4+x/7
4+ -14/7
4+-2
2
Answer:
[tex]4 +\frac{x}{7}=2[/tex]
[tex]\frac{28 + x}{7} = 2[/tex]
28 +x = 14
x =14 - 28
x = -14
Hope this helped.
Step-by-step explanation:
Please help!
What is the median of the data?
Answer:
15 hope it helps:)
Step-by-step explanation:
because it divides 5 in each side
helpp plzz!!! i dont understand
If m+2m+5=14,then m=
Answer:
m=7
Step-by-step explanation:
m +2+5=14
m+7=14
-7 -7
m=7
Can you help me with this question please
Answer:
516
Step-by-step explanation:
First
34% small and 40% large means that 100 - (34 + 40) = 26% medium
26% of 600 = 0.26 × 600 = 156
----------------------------------------------------
Second
[tex]\frac{3}{10}[/tex] are small and [tex]\frac{1}{10}[/tex] are large, which means [tex]\frac{6}{10}[/tex] are medium
[tex]\frac{6}{10}[/tex] × 400 = 0.6 × 400 = 240
-----------------------------------------------------
Third
sum the parts of the ratio, 3 + 4 = 7
Divide 210 by 7 to find the value of one part of the ratio
210 ÷ 7 = 30 ← value of 1 part of ratio
Thus medium = 4 × 30 = 120
Total number of medium packets = 156 + 240 + 120 = 516
I need help understanding this please ASAP!!!
Answer:
13
Step-by-step explanation:
To get the hypotenuse (the longest side) you would use the Pythagorean Theorem ([tex]a^{2} + b^{2} = c^{2}[/tex])
Replace a and b with the two given sides and solve for c
[tex]5^{2} + 12^{2} = c^{2}[/tex]
25 + 144 = [tex]c^{2}[/tex]
169 = [tex]c^{2}[/tex]
Find the square root of both sides
[tex]\sqrt{169} = \sqrt{c^{2}}[/tex]
13 = c
The human population of Earth was approximately 6 billion in 1998. If the rate of
population growth from then on was 2.3% per year, what would be the best
approximation for the human population (in billions) of Earth in 2020?
Answer:
9.89 billion
Step-by-step explanation:
At that rate of growth, the population is multiplied by 1.023 each year. After 22 years, the population would be ...
6·1.023^22 ≈ 9.89 . . . billion
Answer:
Let the equation for the population (P) growth be given by
P = P0ert, where P0 is the initial population in billioins at time t,
t is the number of years since 1987,
r is the rate of growth of population/year
In this case P0 = 5 billion and r = 0.02. Putting these values into the equaation:
P = 5e0.02t
Year 1995 is 8 years after 1987, then the population would be
P = 5e0.02*8 = 5e0.16 ≈ 5.87 billion people
Step-by-step explanation:
If the measure of Angle C A E is 95°, what is the measure of Arc C B A?
90°
95°
190°
195°
Answer: the answer is 190
Step-by-step explanation: I multiplied 95 by two
Answer:
C) 190
Step-by-step explanation:
Divide.
0.45 ÷ 105
A) 0.00045
B) 0.000045
C) 0.0000045
D) 0.00000045
Answer:
0.00045 (A)
Step-by-step explanation:
Answer:
A) 0.00045
Step-by-step explanation:
An interior angle and an adjacent exterior angle of a polygon form a linear pair.
How can you use this fact as another method to find the measure of each exterior
angle in Example 6?
Answer:
30°
Step-by-step explanation:
Interior angle + exterior angle = 180
Because they form a linear pair.
Exterior angle = 180 - interior angle
= 180 - 150
= 30°
The measure of each exterior angle is 30°.
What are Alternate Interior Angles?Alternate Interior Angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles. These angles are always equal.
Given that the measure of each Interior angle is 150°
We have to determine the measure of each exterior
Since an interior angle and an adjacent exterior angle of a polygon form a linear pair.
Therefore, the sum of the Interior angle and exterior angle adds up to 180°.
So Exterior angle = 180 - interior angle
⇒ Exterior angle = 180 - 150
⇒ Exterior angle = 30°
Hence, the measure of each exterior angle is 30°.
Learn more about Alternate Interior Angles here:
brainly.com/question/2125016
#SPJ6
Here are six number cards.
-7 -5 -3 3 1 -1
Arrange the cards into three pairs with the same total.
Answer:
-7 3=-4
-5 1=-4
-3 -1=-4
-7 and 3 make -4. -5 and 1 make -4. -3 and -1 make -4.
The three pairs with the same total are as follow:
-7 + (3) = -4-5 + 1 = -4-3 -1 = -4What are integers?An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043. A set of integers, which is represented as Z, includes:
Positive Numbers: A number is positive if it is greater than zero. Example: 1, 2, 3 . . .Negative Numbers: A number is negative if it is less than zero. Example: -1, -2, -3 . . .Zero is defined as neither a negative number nor a positive number. It is a whole number.Given:
Number on cards -7 -5 -3 3 1 -1
Now, we have to make the pair according it gives the same total
-7 + (3) = -4
-5 + 1 = -4
-3 -1 = -4
Learn more about integers here:
https://brainly.com/question/15276410
#SPJ2
If a coin is flipped 12 times in a row, what is the
probability of landing on heads every time?
A- 1/512
B- 1/4096
C- 1/1024
D- 1/2048
Answer:
b
Step-by-step explanation:
The graph shows f(x) = (x - 5)2. What is the value of h?
h=
Answer:
-5
Step-by-step explanation:
H is the value that is being added or subtracted from x in the equation
f(x)=a(x-h)^2 +k
There are 5280 feet in 1 mile. How many inches are in 4 feet
Answer:
253,440
Step-by-step explanation:
12inches make a foot
So, in 1 miles, total inches equal
5280 × 12 = 63360 inches in one mile
In 4 miles then, total inches would be
63360 × 4 = 253440 inches